The Importance of Tie-Breaking in Finite-Blocklength Bounds

TL;DR

This paper introduces an improved bound on error probability in channel coding that accounts for likelihood ties, providing more accurate estimates especially for additive channels and linear codes.

Contribution

It develops a refined maximum-likelihood union bound considering likelihood ties, enhancing the accuracy of error probability bounds in finite-blocklength channel coding.

Findings

The new bound improves upon previous bounds in finite-blocklength regimes.

Likelihood ties significantly impact error probability estimates.

Simplifications occur for additive channels with linear codes.

Abstract

We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors. We compare this bound to various previous results, both qualitatively and quantitatively. With respect to maximal error probability of linear codes, we observe that when the channel is additive, the derivation of bounds, as well as the assumptions on the admissible encoder and decoder, simplify considerably.